While comparing multiple sets of data produced, the uncertainties and repeatability of those data sets were examined first. This examination was able to conclude whether the small differences in the drag coefficient were from the addition of the airvanes or the error in software used to find the solutions. Appendix E contains the raw data collected from the simulations which were run for the calibration tests. This data, as stated in the previous section, was run on the first set of tests in the parameter study; the change in the angle between the line tangent to the curved portion of the airvane and the line on the horizontal.
The raw data includes the drag coefficients that were calculated during the simulations and the percent reductions in the drag coefficient. Percent reductions were calculated between the drag coefficient calculated for the bus without an airvane attached and the drag coefficient found for each bus model with the airvane attached, including the angle changes.
To determine the repeatability runs were compared to like runs, meaning the RKE turbulence model employing the polyhedral mesh in the first run was compared to the RKE turbulence model employing the polyhedral mesh in the second run. This was repeated for the RKE turbulence model employing the CutCell mesh, the SST model employing the polyhedral mesh, and lastly the SST model employing the CutCell mesh. Polyhedral RKE calibration simulations were analyzed first. Figure 16 illustrates a graph of the drag coefficients found during the simulations versus the angle the airvane was set to, for both the first and second run. The blue line was the first calibration run, while the red line represents the second calibration run.
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Figure 16: Calibration tests run for the Realizable k-ε turbulence model utilizing a polyhedral mesh. This graph represents drag coefficients found in simulations for varying angles between the line tangent to the curved portion of the airvane and the line on the horizontal. The blue line represents the first run of the simulations
and the red line represents the second run of the calibration simulations.
Regarding Figure 16, it can be observed that the first and second calibrations runs were nearly identical. If there was a error in the Fluent simulations the two graphs would not be identical, showing a slight difference in values. The average standard deviation between runs for the coefficient of drag was found to be ± 0.00006. Convergence criterion was set to 1E-5, therefore it could be assumed that the standard deviation for this combination of mesh and turbulence model was very small. These observations, in cohesion, determined that when employed together, the polyhedral mesh and the RKE turbulence model, were almost completely repeatable and the amount of uncertainty present in the simulations was negligible.
A combination of CutCell mesh and RKE turbulence model was the next set of simulations to be analyzed. Figure 17 displays the calibration for these simulations. The blue line represents the first set of simulations run and the red line was the second set of simulations run. The graph represents the drag coefficient found from Fluent simulations versus the angle that the airvane was changed to.
0.586 0.588 0.59 0.592 0.594 0.596 0.598 0.6 0.602 0.604 0.606 0.608
30 50 70 90
Drag Coefficient
Angle (Degrees)
Polyhedral RKE
First Run Secoond Run
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Figure 17: Calibration tests run for the Realizable k-ε turbulence model utilizing a CutCell mesh. This graph represents the drag coefficients found in the simulations for the angle changes between the line tangent to the
curved portion of the airvane and the line on the horizontal. The blue line represents the first run of the simulations and the red line represents the second run of the calibration simulations.
Analyzing the average standard deviation between the runs in Figure 17 provided an error of ± 0.00009. Observing the graph it was perceived that the two calibrations runs were nearly identical. The low average standard deviation and the nearly identical graph led to the conclusion that the error involved in determining the drag coefficient using a CutCell mesh and RKE turbulence model was nearly negligible. Furthermore, based on the information examined in both Figure 16 and Figure 17 it was determined that when using the RKE turbulence model the type of mesh utilized had very little effect on the error in the calculations performed by Fluent. It was established that the RKE turbulence model was significantly repeatable and therefore, drag coefficients calculated by Fluent were accurate and able to be compared directly, without the uncertainties of the drag coefficients making it difficult to determine the optimal dimensions for each parameter.
After analysis of the RKE turbulence model was performed the SST turbulence model was examined. A polyhedral mesh was the first mesh employed and the calibration runs that were completed can be observed in Figure 18. The relationship between the drag coefficient and angle utilized in the airvane is observed in this graph and the blue line signifies the first set of simulations run, while the red line the second set of calibration simulations run.
0.582 0.584 0.586 0.588 0.59 0.592 0.594 0.596 0.598 0.6 0.602 0.604
30 40 50 60 70 80 90
Drag Coefficient
Angle (Degrees)
CutCell RKE
First Run Second Run
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Figure 18: Calibration tests run for the SST k-ω turbulence model utilizing a polyhedral mesh. This graph represents drag coefficients found in simulations run for varying angles between the line tangent to the curved portion of the airvane and the line from the horizontal. The blue line represents the first run of the simulations
and the red line represents the second run of the calibration simulations.
It can be observed, although not as repeatable as the polyhedral RKE calibration, shown in Figure 16, the polyhedral SST calibration run was also highly repeatable. The two sets of simulations run for this combination were nearly identical. An average standard deviation of ± 0.00023 in drag coefficients was calculated between the two sets of simulations. This standard deviation is slightly higher than the ± 0.00006 that was found for the polyhedral RKE calibration. This again implies that the SST turbulence model, although highly repeatable was not as repeatable as the RKE turbulence model.
A CutCell mesh employed with the SST turbulence model was the last set of calibration simulations run. The two sets of simulations that were used in this calibration can be seen in Figure 19. Represented in this graph is the drag coefficient due to the angle that was employed on the airvane. In this graph the solid blue line was the first run, while the dotted red line was the second set of simulations run.
0.6 0.605 0.61 0.615 0.62 0.625
30 40 50 60 70 80 90
Drag Coefficient
Angle (Degrees)
Polyhedral SST
First Run Second Run
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Figure 19: Graph of calibration tests run for the SST k-ω turbulence model utilizing a CutCell mesh. This graph represents drag coefficients found in simulations run for angles tested between the line tangent to the curved portion of the airvane and the line on the horizontal. The blue line represents the first run of the
simulations and the red line represents the second run of the calibration simulations.
When compared, as shown in Figure 19, the SST turbulence model when employed with a CutCell mesh was found to be highly repeatable. The drag coefficients found for both sets of simulations were nearly identical for every set angle. The standard deviation for the drag coefficient was calculated to be ± 0.00034. Being higher that the standard deviation of ± 0.00009 associated with the CutCell RKE simulations, it again can be deduced that the RKE turbulence model is more repeatable, but the SST turbulence model is also adequate in determining the optimal dimension when running the parameter studies without the need to consider the uncertainty.
When analyzing the meshes themselves, apart from the turbulence models, it could be observed that the standard deviations for the simulations using the CutCell mesh were slightly higher than the simulations employing the polyhedral mesh. With this observation it could be determined that the polyhedral mesh was marginally more repeatable that the CutCell mesh. Due to the fact that the errors in Fluent simulations were almost negligible the errors were not considered when examining the drag coefficients and percent reductions found
0.58 0.585 0.59 0.595 0.6 0.605 0.61 0.615
30 40 50 60 70 80 90
Drag Coefficent
Angle (Degrees)
CutCell SST
Frist Run Second Run
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